A Lévy process approach coupled to the stochastic Leslie–Gower model

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dc.citation.epage188
dc.citation.issue11
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage178
dc.citation.volume1
dc.contributor.affiliationУніверситет Абдельмалека Ессааді
dc.contributor.affiliationУніверситет Мухаммеда V у Рабаті
dc.contributor.affiliationAbdelmalek Essaadi University
dc.contributor.affiliationMohammed V University in Rabat
dc.contributor.authorБен Саїд, М.
dc.contributor.authorАгутан, Н.
dc.contributor.authorАзрар, Л.
dc.contributor.authorBen Said, M.
dc.contributor.authorAghoutane, N.
dc.contributor.authorAzrar, L.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T07:44:11Z
dc.date.created2024-02-24
dc.date.issued2024-02-24
dc.description.abstractСтаття присвячена двовимірній стохастичній системі хижак-жертва з неперервним часом Леслі-Гроуера та стрибками Леві. Спершу доведено, що існує єдиний позитивний розв'язок системи з позитивним початковим значенням. Потім встановлено достатні умови для середньої стійкості та зникнення розглянутої системи. Розроблено числові алгоритми вищого порядку. Отримані результати показують, що стрибки Леві суттєво змінюють властивості популяційних систем.
dc.description.abstractThis paper focuses on a two-dimensional Leslie–Grower continuous-time stochastic predator–prey system with Lévy jumps. Firstly, we prove that there exists a unique positive solution of the system with a positive initial value. Then, we establish sufficient conditions for the mean stability and extinction of the considered system. Numerical algorithms of higher order are elaborated. The obtained results show that Lévy jumps significantly change the properties of population systems.
dc.format.extent178-188
dc.format.pages11
dc.identifier.citationBen Said M. A Lévy process approach coupled to the stochastic Leslie–Gower model / M. Ben Said, N. Aghoutane, L. Azrar // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 178–188.
dc.identifier.citationenBen Said M. A Lévy process approach coupled to the stochastic Leslie–Gower model / M. Ben Said, N. Aghoutane, L. Azrar // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 178–188.
dc.identifier.doi10.23939/mmc2024.01.178
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113777
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 11 (1), 2024
dc.relation.ispartofMathematical Modeling and Computing, 11 (1), 2024
dc.relation.references[1] Liu M., Wang K. Survival analysis of a stochastic cooperation system in a polluted environment. Journal of Biological Systems. 19 (02), 183–204 (2011).
dc.relation.references[2] Lipster R. Sh. A strong law of large numbers for local martingales. Stochastics. 3 (1–4), 217–228 (1980).
dc.relation.references[3] Lotka A. J. The Elements of Physical Biology. Williams and Wilkins, Baltimore (1925).
dc.relation.references[4] Leslie P. H. Some further notes on the use of matrices in populationmathematic. Biometrica. 35 (3–4), 213–245 (1948).
dc.relation.references[5] Leslie P. H., Gower J. C. The properties of a stochastic model for the predator-prey type of interaction between two species. Biometrica. 47 (3–4), 219–234 (1960).
dc.relation.references[6] Korobeinikov A. A Lyapunov function for Leslie–Gower predator–prey models. Applied Mathematics Letters. 14 (6), 697–699 (2001).
dc.relation.references[7] Lahrouz A., Ben Said M., Azrar L. Dynamical Behavior Analysis of the Leslie–Gower Model in Random Environment. Differential Equations and Dynamical systems. 30, 817–843 (2022).
dc.relation.references[8] Bao J., Mao X., Yin G., Yuan C. Competitive Lotka–Volterra population dynamics with jumps. Nonlinear Analysis: Theory, Methods & Applications. 74 (17), 6601–6616 (2011).
dc.relation.references[9] Applebaum D. L´evy Processes and Stochastics Calculus. Cambridge University Press (2009).
dc.relation.references[10] Kunita H. Itˆo’s stochastic calculus: Its surprising power for applications. Stochastic Processes and their Applications. 120 (5), 622–652 (2010).
dc.relation.references[11] Luo Q., Mao X. Stochastic population dynamics under regime switching. Journal of Mathematical Analysis and Applications. 334 (1), 69–84 (2007).
dc.relation.references[12] Ikeda N., Wantanabe S. Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam (1981).
dc.relation.references[13] Bao J., Mao X., Yin G., Yuan C. Competitive Lotka–Volterra population dynamics with jumps. Nonlinear Analysis: Theory, Methods & Applications. 74 (17), 6601–6616 (2011).
dc.relation.references[14] Luo Q., Mao X. Stochastic population dynamics under regime switching. Journal of Mathematical Analysis and Applications. 334 (1), 69–84 (2007).
dc.relation.references[15] Polasek W., Shaparova E. Numerical Solution of Stochastic Differential Equations with Jumps in Finance by Eckhard Platen, Nicola Bruti–Liberati. International Statistical Review. 81 (2), 307–335 (2013).
dc.relation.referencesen[1] Liu M., Wang K. Survival analysis of a stochastic cooperation system in a polluted environment. Journal of Biological Systems. 19 (02), 183–204 (2011).
dc.relation.referencesen[2] Lipster R. Sh. A strong law of large numbers for local martingales. Stochastics. 3 (1–4), 217–228 (1980).
dc.relation.referencesen[3] Lotka A. J. The Elements of Physical Biology. Williams and Wilkins, Baltimore (1925).
dc.relation.referencesen[4] Leslie P. H. Some further notes on the use of matrices in populationmathematic. Biometrica. 35 (3–4), 213–245 (1948).
dc.relation.referencesen[5] Leslie P. H., Gower J. C. The properties of a stochastic model for the predator-prey type of interaction between two species. Biometrica. 47 (3–4), 219–234 (1960).
dc.relation.referencesen[6] Korobeinikov A. A Lyapunov function for Leslie–Gower predator–prey models. Applied Mathematics Letters. 14 (6), 697–699 (2001).
dc.relation.referencesen[7] Lahrouz A., Ben Said M., Azrar L. Dynamical Behavior Analysis of the Leslie–Gower Model in Random Environment. Differential Equations and Dynamical systems. 30, 817–843 (2022).
dc.relation.referencesen[8] Bao J., Mao X., Yin G., Yuan C. Competitive Lotka–Volterra population dynamics with jumps. Nonlinear Analysis: Theory, Methods & Applications. 74 (17), 6601–6616 (2011).
dc.relation.referencesen[9] Applebaum D. L´evy Processes and Stochastics Calculus. Cambridge University Press (2009).
dc.relation.referencesen[10] Kunita H. Itˆo’s stochastic calculus: Its surprising power for applications. Stochastic Processes and their Applications. 120 (5), 622–652 (2010).
dc.relation.referencesen[11] Luo Q., Mao X. Stochastic population dynamics under regime switching. Journal of Mathematical Analysis and Applications. 334 (1), 69–84 (2007).
dc.relation.referencesen[12] Ikeda N., Wantanabe S. Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam (1981).
dc.relation.referencesen[13] Bao J., Mao X., Yin G., Yuan C. Competitive Lotka–Volterra population dynamics with jumps. Nonlinear Analysis: Theory, Methods & Applications. 74 (17), 6601–6616 (2011).
dc.relation.referencesen[14] Luo Q., Mao X. Stochastic population dynamics under regime switching. Journal of Mathematical Analysis and Applications. 334 (1), 69–84 (2007).
dc.relation.referencesen[15] Polasek W., Shaparova E. Numerical Solution of Stochastic Differential Equations with Jumps in Finance by Eckhard Platen, Nicola Bruti–Liberati. International Statistical Review. 81 (2), 307–335 (2013).
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectЛеслі–Гауер
dc.subjectSDEs
dc.subjectформула Іто
dc.subjectзагасання
dc.subjectстохастична модель “хижак–жертва”
dc.subjectметод Тейлора
dc.subjectLeslie–Gower
dc.subjectSDEs
dc.subjectItˆo’s formula
dc.subjectextinction
dc.subjectstochastic predator–prey model
dc.subjectTaylor method
dc.titleA Lévy process approach coupled to the stochastic Leslie–Gower model
dc.title.alternativeПідхід на основі процесу Леві в поєднанні зі стохастичною моделлю Леслі–Гауера
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 1